Answer:
<em>The approximate percentage of women with platelet counts between 127.7 and 378.5 </em>
<em>P( 127.7 ≤x≤378.5) = 0.9544 or 95 percentage</em>
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
<em>Mean of the Population = 253.1</em>
<em>Given standard deviation of the Population = 62.7</em>
<em>Given sample size 'n' = 873</em>
<em>Let 'X' be the random variable in Normal distribution</em>
<em>Let x₁ = 127.7</em>
Let x₂ = 378.5
<u><em>Step(ii)</em></u>:-
<em>The probability of women with platelet counts between 127.7 and 378.5.</em>
<em>P( 127.7 ≤x≤378.5) = P( -2≤Z≤2)</em>
<em> =</em> P(<em>Z≤2) - P(Z≤-2)</em>
<em> = 0.5 +A(2) - ( 0.5 - A(-2))</em>
<em> = A(2) + A(2) (∵A(-2) =A(2)</em>
<em> = 2 × A(2)</em>
<em> = 2× 0.4772</em>
<em> = 0.9544</em>
<u><em>Conclusion</em></u><em>:-</em>
<em>The approximate percentage of women with platelet counts between 127.7 and 378.5 is 0.9544 or 95 percentage</em>